How can I fill the inside of this helmet?
So my answer works better if you've kept a low-poly version. Always keep a low-poly version somewhere, before applying the Subdivision Surface.
You can:

Select all the external vertices + the small inner extrusions:



Press Ctrli to invert the selection:



Delete:



Fill the gaps, with Grid Fill if possible:



For the bottom, extrude inwards and close the shape: